Overcoming network resilience to synchronization through non-fast stochastic broadcasting.

Stochastic broadcasting is an important and understudied paradigm for controlling networks. In this paper, we examine the feasibility of on-off broadcasting from a single reference node to induce synchronization in a target network with connections from the reference node that stochastically switch in time with an arbitrary switching period. Internal connections within the target network are static and promote the network's resilience to externally induced synchronization. Through rigorous mathematical analysis, we uncover a complex interplay between the network topology and the switching period of stochastic broadcasting, fostering or hindering synchronization to the reference node. We derive a criterion which reveals an explicit dependence of induced synchronization on the properties of the network (the Laplacian spectrum) and the switching process (strength of broadcasting, switching period, and switching probabilities). With coupled chaotic tent maps as our test-bed, we prove the emergence of "windows of opportunity" where only non-fast switching periods are favorable to synchronization. The size of these windows of opportunity is shaped by the Laplacian spectrum such that the switching period needs to be manipulated accordingly to induce synchronization. Surprisingly, only the zero and the largest eigenvalues of the Laplacian matrix control these windows of opportunities for tent maps within a wide parameter region.